What's up in

Mathematicians have had a hard time finding commonalities in large groups of random shapes — until recently.

Researchers have uncovered deep connections among different types of random objects, illuminating hidden geometric structures.

Peter Scholze is a favorite to win one of the highest honors in mathematics for his contributions in number theory and geometry.

At 28, Peter Scholze is uncovering deep connections between number theory and geometry.

The Ukrainian mathematician Maryna Viazovska has solved the centuries-old sphere-packing problem in dimensions eight and 24.

Assigning elements from a large collection to one of two categories can yield almost “magical” predictions about highly complicated problems without actually solving them.

In a geometrically designed social club, how do dancing, triangles and hexagons mix?

The mathematician John Horton Conway’s myriad accomplishments — including the Game of Life, sprouts and the surreal numbers — are the product of a mind at play.

Mathematicians have solved the century-old triangulation conjecture, a major problem in topology that asks whether all spaces can be subdivided into smaller units.